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Hello! Was wondering what is the domain of this problem and the domains restriction with a one sentence explanation. Thank you!

Hello! Was wondering what is the domain of this problem and the domains restriction-example-1
User Cnicutar
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1 Answer

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6 votes

Solution


\begin{gathered} Given \\ (-10t^2+50t)/(t^2+4t+3) \\ \end{gathered}
\begin{gathered} (-10t^2+50t)/(t^2+4t+3)\text{ =}(-10t^2+50t)/(t^2+3t+t+3) \\ =(-10t^2+50t)/(t(t+3)+1(t+3)) \\ =(-10t^2+50t)/((t+3)(t+1)) \end{gathered}

Set the denominator to zero


\begin{gathered} (t+3)(t+1)=0 \\ t+3=0,\text{ or t+1=0} \\ t=-3\text{ or t=-1} \end{gathered}

The domain of a function is the set of input values for which the function is real and defined.

Thus, the domain of the function is

t < -3, or -3 < t < -1 or t > -1

The domain restrictions are the value of t for which the function is undefined or not real

Thus, The domains restriction is t = -3 or t = -1

User Lino
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